how to factor this expression step by step

Question

3x²-7x-6

Answer 1

Let's look at (Ax² +Bx + C).  Since A is 3, it will look something like this:

(3x    )(x   ).  To find out those missing numbers, we have to look at C value: -6.

 

Since C is negative, you know that one of them must be negative.  It is either 6&1 or 3&2. 

How to find which one fits that? look at each binomials: (3x   ) and (x   ).  If you use 6&1, the middle term will be either +17, -17 (if 6 is with x and 1 is with 3x)) or +9, -9 (if 6 is with 3x and 1 is with x) so this will not work.

 

3&2.  As you use 3 and 2, you can see that 3 & 3 makes 9 and 1 & 2 makes 2 to make 7.  How to put them in right place? since 3 has to be multiplied, 3 must go with x and 2 must go with 3x.  So it will look something like this:

(3x   2) (x   3).  How to figure out the signs? (remember, one of them must be negative because C is negative) compare the 3x * 3 and 2 * x.  Since middle term is negative, the bigger one gets - sign.  So, how to make -7x between 9x & 2x? -9x + 2x.  So, final answer look like this:

 

(3x+2) (x-3). 

 

That 3 has to be outside because it has to be multiplied.  If the 3 stayed with 3x or stayed inside, it becomes one term.  If terms and numbers wants to be multiplied, they must be separated or it will be known as one term.

 

A lot of people will "grouping method" to be easy but I rather go through trial and error because it builds more depths and experience.  And "grouping method" catch people off guard if big number comes up.

 

Good luck.